A Yaglom type asymptotic result for subcritical branching Brownian motion with absorption

Abstract

We consider a slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motions with drift $-\sqrt{2+2\epsilon }$, undergo dyadic fission at rate $1$, and are killed when they reach the origin. We obtain a Yaglom type asymptotic result, showing that the long run expected number of particles conditioned on survival grows exponentially as $1/\sqrt{\epsilon }$ as the process approaches criticality.

30 pages

References in corpus (1)

• The survival probability of a branching random walk in presence of an absorbing wall